Effective Properties and Energy Methods in Thermoelasticity of Composite Materials

We now summarize the principal formulae of thermoelastostatics of statistically homogeneous composites satisfying the ergodicity condition in a form that is appropriate for our intended application to composites [251], [302], [438], [439], [460], [602], [646], [1180], [1183]. General representations of both effective properties and effective energy functions are presented through the local stress and strain concentrator factors. Some general exact results for both the two-phase composites and polycrystals composed of transversally isotropic crystals are presented. We will consider the variational methods representing the most rigorous trend of micromechanics which generate the bounds of effective properties by the substitution of approximate fields into the strict energy bounds obtained by the volume average of the energy density with the help of lower-order correlation functions.